Missing Data Assumptions

I review assumptions about the missing-data mechanisms that underlie methods for the statistical analysis of data with missing values. I describe Rubin's original definition of missing at random (MAR), its motivation and criticisms, and his sufficient conditions for ignoring the missingness mechanism for likelihood-based, Bayesian, and frequentist inference. Related definitions, including missing completely at random, always MAR, always missing completely at random, and partially MAR, are also covered. I present a formal argument for weakening Rubin's sufficient conditions for frequentist maximum likelihood inference with precision based on the observed information. Some simple examples of MAR are described, together with an example where the missingness mechanism can be ignored even though MAR does not hold. Alternative approaches to statistical inference based on the likelihood function are reviewed, along with non-likelihood frequentist approaches, including weighted generalized estimating equations. Connections with the causal inference literature are also discussed. Finally, alternatives to Rubin's MAR definition are discussed, including informative missingness, informative censoring, and coarsening at random. The intent is to provide a relatively nontechnical discussion, although some of the underlying issues are challenging and touch on fundamental questions of statistical inference.

Automated summary

This paper reviews assumptions about missing data mechanisms and discusses statistical analysis methods related to missing data, including Rubin's MAR definition and its limitations, as well as some sufficient conditions. It also explores other definitions and methods related to missing data, and presents an argument for weakening the conditions for frequentist maximum likelihood inference.